Enhanced inertial system performance

ABSTRACT

An inertial system is provided. The system includes at least one inertial sensor, a processing unit and a plurality of Kalman filters implemented in the processing unit. The Kalman filters receive information from the at least one inertial sensor. At most one of the plurality of Kalman filters has processed zero velocity updates on the last cycle.

RELATED APPLICATION(S)

The present application is a continuation application of U.S.application Ser. No. 11/215,762 (the '762 Application), filed Aug. 30,2005 (pending). The '762 Application is incorporated herein byreference.

TECHNICAL FIELD

The present invention relates generally to inertial systems and inparticular to the use of Kalman filters to improve inertial systems.

BACKGROUND

Some inertial measurement systems are used to determine the attitude andpropagate the position of an object on the ground. This is done byutilizing inertial sensors which measure rate information of the objectrelative to an inertial frame of reference. An inertial frame ofreference is constant with respect to inertial space. Non-inertialframes of reference, such as an earth fixed frame, rotate and possiblytranslate with respect to an inertial frame. An example of an inertialsensor is an accelerometer which measures the change of velocity withrespect to an inertial frame. Inertial sensors can be used by aninertial measurement system to realize 3-dimensional coordinates for theposition of the object. To increase the accuracy of the coordinates,only the components of the body-sensed measurements which are relativeto the actual motion of the vehicle are measured, and earth rotation,vibrations, and other random errors are eliminated.

Kalman filters are used by systems such as an inertial measurementsystem to estimate the state of a system from measurements, such asthose from inertial sensors. Inertial sensor measurements are integratedup and contain random errors that the Kalman filter estimates in orderto determine the attitude of the object. The accuracy of the positiondetermined by an inertial system is dependent on processing zerovelocity updates (ZUPTS). ZUPTS are measurements made by inertialsensors while the vehicle is stopped to ensure the accuracy of theposition of the vehicle. ZUPTS are accurate only when the vehicle isstopped. When the vehicle moves, processing an observation to the Kalmanfilter that assumes the vehicle is stopped causes an error in theinertial measurement system. Detection of motion that would enable thesystem to avoid erroneous ZUPTS often occurs after the motion hasstarted.

Techniques of detecting motion generally involve the use of a threshold.Unfortunately, in order to detect the motion as soon as possible thethreshold level is reduced to a degree where vibrations, and not actualmovement, have caused the threshold to be exceeded. Also, thesetechniques detect motion after it is started and allow erroneous ZUPTSto be processed.

For the reasons stated above and for other reasons stated below whichwill become apparent to those skilled in the art upon reading andunderstanding the present specification, there is a need in the art fora method of removing possible errors caused by incorrect zero velocityupdates processed by Kalman filters.

SUMMARY

The present application relates to an inertial system. The inertialsystem includes at least one inertial sensor; a processing unit; and aplurality of Kalman filters implemented in the processing unit. Theplurality of Kalman filters receive information from the at least oneinertial sensor. At most one of the plurality of Kalman filters hasprocessed zero velocity updates on the last cycle.

The above-mentioned problems and other problems are resolved by thepresent invention and will be understood by reading and studying thefollowing specification.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be more easily understood and furtheradvantages and uses thereof more readily apparent, when considered inview of the description of the preferred embodiments and the followingfigures in which:

FIG. 1 is an inertial system of one embodiment of the present invention.

FIG. 2 is a flow chart of one embodiment of a method of the presentinvention.

FIG. 3 is a view of one embodiment of a method of the present invention.

FIG. 4 is a block diagram of a vehicle of one embodiment of the presentinvention.

FIG. 5 is an inertial navigation system of one embodiment of the presentinvention.

DETAILED DESCRIPTION

In the following detailed description of the preferred embodiments,reference is made to the accompanying drawings, which form a parthereof, and in which is shown by way of illustration specific preferredembodiments in which the inventions may be practiced. These embodimentsare described in sufficient detail to enable those skilled in the art topractice the invention, and it is to be understood that otherembodiments may be utilized and that logical, mechanical and electricalchanges may be made without departing from the spirit and scope of thepresent invention. The following detailed description is, therefore, notto be taken in a limiting sense, and the scope of the present inventionis defined only by the claims and equivalents thereof.

Embodiments of the present invention include an inertial system withimproved accuracy by having a plurality of Kalman filters. The pluralityof Kalman filters includes one that has processed zero velocity updates(ZUPTS) on the last cycle and at least one that has not processed ZUPTSon the last cycle but has processed ZUPTS on at least one previouscycle. When motion is detected, the inertial system can revert back tothe solution maintained by a Kalman filter that has not processed ZUPTSon the last cycle (or has not processed ZUPTS on multiple cycles),thereby removing bad observations due to ZUPTS processed when thevehicle was in motion.

In another embodiment, the method of detecting motion using the multipleKalman filters is enhanced. This is done by using a solution separationalgorithm which is beneficial for detecting motion in slow movingobjects. This technique overcomes problems with conventional thresholdmotion detection algorithms as applied to, for example, slow movingobjects.

In another embodiment, a vehicle incorporating an inertial system with aplurality of Kalman filters is provided. The vehicle includes a guidancesystem and a position controller than moves the vehicle to the properposition.

FIG. 1 is an inertial system of one embodiment of the present inventionshown generally at 100. Inertial system 100 is comprised of inertialsensor 102. In one embodiment, inertial sensor 102 is an accelerometer.In another embodiment, inertial sensor 102 is a gyroscope. In anotherembodiment, inertial sensor 102 is a plurality of accelerometers or aplurality of gyroscopes or a combination of the two. Inertial sensor 102is used in civil and military aviation, missiles and other projectiles,submarines and space technology as well as a number of other vehicles.Inertial sensor 102 measures rotational and linear movements withoutreference to external coordinates. For example, accelerometers measure achange of velocity with respect to an inertial frame. Gyroscopes measurechange of rotation with respect to inertial space. Inertial sensor 102is subject to errors such as vibration and other disturbances.

Inertial sensor 102 communicates with a processing unit 104 via acommunication link 108. In one embodiment, communication link 108 iswireless. In another embodiment, communication link 108 is a wiredconnection. Processing unit 104 includes but is not limited to digitalelectronic circuitry, a programmable processor (for example, aspecial-purpose processor or a general-purpose processor such as acomputer) firmware, software, or in combinations of them.

Processing unit 104 implements a plurality of Kalman filters 106-1 . . .106-N. Kalman filters 106-1 . . . 106-N, in general terms, estimate aseries of parameters that describe and predict the behavior of a system.The Kalman filters 106-1 . . . 106-N operate with a set of statevariables that describe errors in the system and an associatedcovariance matrix that describes the current knowledge level of thestate. The Kalman filters 106-1 . . . 106-N maintain an estimate of thesystem errors and associated covariance over time and in the presence ofexternal measurements through the use of propagation and updatingprocesses. Kalman filters 106-1 . . . 106-N take the informationprovided by the inertial sensor 102 and received by the processing unit104, including the errors created when they are integrated, and providesan estimate of the position, velocity, and attitude of the vehicle.

The accuracy of the position of the inertial system 100 is dependent onthe Kalman filters 106-1 . . . 106-N processing zero velocityobservations (ZUPTS). ZUPTS are only accurate when the vehicle isstopped. When the vehicle moves, processing an observation to the Kalmanfilters 106-1 . . . 106-N that assumes the vehicle is stopped causes anerror. Detection of motion that allows the system 100 to avoid erroneousZUPTS often occurs after the motion has started. This detection ofmotion is performed by the processing unit 104 using a motion detectionalgorithm. In one embodiment, the motion detection algorithm is athreshold algorithm. In another embodiment, the motion detectionalgorithm is a solution separation algorithm as described below in FIG.3. To avoid erroneously processing ZUPTS system 100 maintains aplurality of Kalman filters 106-1 . . . 106-N that have processed zerovelocity updates on various cycles.

In one embodiment, Kalman filter 106-1 processes ZUPTS on all thecycles, and Kalman filter 106-N does not process ZUPTS on the lastcycle. This allows the processing unit 104 to revert back to Kalmanfilter 106-N which did not process ZUPTS on the last cycle when motionis detected. This reduces the likelihood that the ZUPTS processed willhave errors due to vehicle movement.

In one embodiment, N is equal to two and Kalman filter 106-2 does notprocess ZUPTS on the last cycle as described above. In anotherembodiment, N is greater than two and for each additional Kalman filter106-1 . . . 106-N there is an additional cycle where ZUPTS are notprocessed. For example, when N is equal to four, Kalman filter 106-1processes ZUPTS on all cycles, Kalman filter 106-2 does not processZUPTS on the last cycle, Kalman filter 106-3 does not process ZUPTS onthe last two cycles, and Kalman filter 106-4 does not process ZUPTS onthe last three cycles. In one embodiment, a cycle is approximately equalto one second. The length of a cycle and the number of Kalman filters106-1 . . . 106-N are application dependent. One embodiment of a processfor preventing erroneous processing of ZUPTS is described with respectto FIG. 2 below.

FIG. 2 is a flow chart of one embodiment of a method of improving theaccuracy of an inertial system shown generally at 200. A plurality ofKalman filters is initialized and the cycle starts (202). A plurality ofKalman filters are used because when a vehicle moves, processing anobservation to the Kalman filters that assumes the vehicle is stoppedcauses an error. Detection of motion that allows the system 200 to avoiderroneous ZUPTS often occurs after the motion has started. Therefore,the method maintains a plurality of Kalman filters that have processedzero velocity updates on various cycles in order to revert back to aKalman filter that processed zero velocity updates when no motionoccurred.

In this embodiment, Kalman filter 1 represents the Kalman filter thatprocesses ZUPTS on all cycles. Kalman filter N represents the Kalmanfilter that has not processed ZUPTS when motion was occurring. In oneembodiment, Kalman filter N did not process ZUPTS on the last cycle. Inanother embodiment, Kalman filter N did not process ZUPTS on a number ofsequential cycles.

The plurality of Kalman filters form non-zero velocity updates (ZUPTS)observations (204). These non-ZUPT observations are for the measurementvector (z) and the measurement sensitivity matrix (H) (204). Each of theplurality of Kalman filters are updated (206). The following list ofequations describes this update process.

P _(i) =ΦP _(i)Φ^(T) +Q

X_(i)=ΦX_(i)

K _(i) =P _(i) H ^(T) [HP _(i) H ^(T) +R] ⁻¹

P _(i)=[1−K _(i) H]P _(i)

X _(i) =X _(i) +K[z−HX _(i)]

P_(i) is the covariance of Kalman filter i.

X_(i) is the error state vector for Kalman filter i.

Φ is the state transition matrix for Kalman filter i.

Q is the process noise for the error states in all Kalman filters.

K_(i) is the measurement gain matrix for the non-ZUPT observations forKalman filter i.

H is the measurement sensitivity matrix for the non-ZUPT observations.

z is the measurement vector for the non-ZUPT observations for Kalmanfilter i.

K_(i) ^(ZUPT) is the measurement gain matrix for the ZUPT observationsfor Kalman filter i.

H^(ZUPT) is the measurement sensitivity matrix for the ZUPTobservations.

z^(ZUPT) is the measurement vector for the ZUPT observations.

The method then determines whether motion has been detected by a motiondetect algorithm (208). In one embodiment, the motion detectionalgorithm uses a threshold to determine if there has been motion. Inanother embodiment, the motion detection algorithm is a solutionseparation algorithm as described below in FIG. 3. If no motion isdetected, then ZUPT observations are formed (z^(ZUPT) and H^(ZUPT))(210).

If no motion is detected, each Kalman filter copies the covariance anderror state vector of the Kalman filter that has processed one morecycle of ZUPTS (212). This process starts with the Kalman filter thathas processed the least amount of ZUPTS and ends when the covariance anderror state vector for the Kalman filter that processed ZUPTS on thelast cycle is copied to the Kalman filter that did not process ZUPTS onthe last cycle (212). In one embodiment, the Kalman filter thatprocessed ZUPTS on the last cycle is Kalman filter 1. After the Kalmanfilters are copied, the zero velocity updates are applied to Kalmanfilter 1 as demonstrated in the following equations (214).

K ₁ ^(ZUPT) =P ₁ [H ^(ZUPT)]^(T) [[H ^(ZUPT) ]P ₁ [H ^(ZUPT)]^(T) +R^(ZUPT)]⁻¹

P ₁ =[I−K ₁ ^(ZUPT) H ^(ZUPT) ]P ₂

where I is an identity matrix.

X ₁ =X ₁ +K ₁ ^(ZUPT) [z ^(ZUPT) −H ^(ZUPT) X ₁]

After the zero velocity updates are applied to Kalman filter 1 the cyclestops (216). If motion was detected, the error state vector andcovariance of Kalman filter N is copied to all the Kalman filtersbecause all of the other Kalman filters erroneously processed ZUPTS whenthe vehicle was in motion (218). After Kalman filter N is copied, thecycle stops (216).

FIG. 3 is a view of one embodiment of a method of the present inventionshown generally at 300. In this embodiment, a solution separationalgorithm 302 is shown. In one embodiment, solution separation algorithm302 is used to detect motion as shown in block 208 of FIG. 2 rather thanusing a threshold method. Motion is assumed to have occurred if theposition separation between a Kalman filter that assumed no motion and aKalman filter that assumed motion is greater than the statisticallyexpected separation. In order to understand the solution separationalgorithm a listing of definitions is provided.

P_(i) (1,1) is the first position error covariance of Kalman filter i.

P_(i) (2,2) is the second position error covariance of Kalman filter i.

P_(i) (3,3) is the third position error covariance of Kalman filter i.

X_(i) (1) is the first position error state estimate of Kalman filter i.

X_(i) (2) is the second position error state estimate of Kalman filteri.

X_(i) (3) is the third position error state estimate of Kalman filter i.

The solution separation algorithm 302 takes the difference between thefirst position error state estimate of the n^(th) Kalman filter and thefirst Kalman filter and squares it. If this number is greater than thedifference between the first position error covariance of the n^(th)Kalman filter and the first Kalman filter multipled by C then motion isimplied. C is defined as the confidence level required for the test. Avalue of C greater than one implies a need for uncertainty associatedwith motion to be greater than one-sigma. This number is applicationdependent.

The solution separation algorithm 302 then takes the difference betweenthe second position error state estimate of the n^(th) Kalman filter andthe first Kalman filter and squares it. If this number is greater thanthe difference between the second position error covariance of then^(th) Kalman filter and the first Kalman filter multipled by C thenmotion is implied.

The solution separation algorithm 302 then takes the difference betweenthe third position error state estimate of the n^(th) Kalman filter andthe first Kalman filter and squares it. If this number is greater thanthe difference between the third position error covariance of the n^(th)Kalman filter and the first Kalman filter multipled by C then motion isimplied.

If any of these equations implies motion, zero velocity observations areformed as shown with respect to block 210 of FIG. 2 above. If however,none of these equations implies motion, then Kalman filter N is copiedto all Kalman filters as shown with respect to block 218 of FIG. 2above.

FIG. 4 is a block diagram of a vehicle of one embodiment of the presentinvention shown generally at 400. Vehicle 400 comprises an inertialsystem 402. Inertial system 402 provides vehicle 400 positioninginformation. Inertial system 402 uses multiple Kalman filters to enablemaintaining a proper output even when ZUPTS are processed when thevehicle is in motion. One example of inertial system 402 is inertialsystem 100 described above in FIG. 1. Another example of inertial system402 is inertial navigation system 500 described below in FIG. 5.Inertial system 402 communicates with a guidance system 404 via acommunication link 408. In one embodiment, communication link 408 iswireless. In another embodiment, communication link 408 is a wiredconnection. Guidance system 404 takes information received from inertialsystem 402 and determines what actions, if any, are necessary tomaintain or achieve a proper heading. When guidance system 404determines a course of action which requires a change in position ofvehicle 400, guidance system 404 communicates with a vehicle positioncontroller 406 via a communication link 410. In one embodiment,communication link 410 is wireless. In another embodiment, communicationlink 410 is a wired connection. Vehicle position controller 406 takesthe information received from guidance system 404 and moves vehicle 400to the appropriate position.

FIG. 5 is an inertial navigation system of one embodiment of the presentinvention shown generally at 500. Inertial navigation system 500 iscomprised of a processor 508. Processor 508 includes navigationequations 510 which receive data from sensors and integrates the databefore sending it to Kalman filters 512. In one embodiment, the sensorsare accelerometers 506. In another embodiment, the sensors aregyroscopes 504. In another embodiment, the sensors are aiding sources502, including but not limited to, global positioning systems (GPS) andodometers.

Accelerometers 506, gyroscopes 504, and aiding sources 502 communicatewith processor 508 via a communication link 514. In one embodiment,communication link 108 is wireless. In another embodiment, communicationlink 514 is a wired connection. Processor 508 includes but is notlimited to digital electronic circuitry, a programmable processor (forexample, a special-purpose processor or a general-purpose processor suchas a computer) firmware, software, or in combinations of them.

Navigation equations 510 send data, including but not limited to,position, velocity, attitude, acceleration, and angular rates to theKalman filters 512. Kalman filters 512 receive the data, and afterperforming calculations, send back to the navigation equations 510 anavigation solution and sensor data corrections.

The accuracy of the data used in inertial navigation system 500 isdependant on processing zero velocity updates (ZUPTS). ZUPTS are onlyaccurate when the vehicle in which the inertial navigation system 500 islocated, is stopped. Inertial navigation system 500 uses multiple Kalmanfilters 512 to enable maintaining a proper output even when ZUPTS areprocessed when the vehicle is in motion. One example of a method ofusing multiple Kalman filters 512 to avoid errors due to processingZUPTS while the vehicle is in motion is described above in FIG. 2.

Although specific embodiments have been illustrated and describedherein, it will be appreciated by those of ordinary skill in the artthat any arrangement, which is calculated to achieve the same purpose,may be substituted for the specific embodiment shown. This applicationis intended to cover any adaptations or variations of the presentinvention. Therefore, it is manifestly intended that this invention belimited only by the claims and the equivalents thereof.

1. An inertial system, the system comprising: at least one inertialsensor; a processing unit; and a plurality of Kalman filters implementedin the processing unit, the plurality of Kalman filters receivinginformation from the at least one inertial sensor, wherein at most oneof the plurality of Kalman filters has processed zero velocity updateson the last cycle.
 2. The system of claim 1, wherein the at least oneinertial sensor is an accelerometer.
 3. The system of claim 1, whereinat least one of the plurality of Kalman filters has not processed zerovelocity updates on the last cycle.
 4. The system of claim 3, whereinthe processing unit copies an error state vector and a covariance of theat least one of the plurality of Kalman filters that has not processedzero velocity updates on the last cycle to the other filters.
 5. Thesystem of claim 3, wherein at least one other of the plurality of Kalmanfilters has not processed zero velocity updates on multiple cycles. 6.The system of claim 5, wherein the processing unit copies an error statevector and a covariance of the at least one other of the plurality ofKalman filters that has not processed zero velocity updates on themultiple cycles to the other filters.
 7. The system of claim 1, whereinat least one of the plurality of Kalman filters has not processed zerovelocity updates on multiple cycles.
 8. A method of generating data inan inertial system, the method comprising: processing multiple Kalmanfilters at a processing unit; determining when motion was occurring; andselecting one of the multiple Kalman filters that did not process zerovelocity updates when motion was occurring.
 9. The method of claim 8,wherein processing the multiple Kalman filters comprises processingmeasurements not associated with zero velocity updates.
 10. The methodof claim 8, wherein processing the multiple Kalman filters comprisesupdating the multiple Kalman filters.
 11. The method of claim 10,wherein updating the multiple Kalman filters comprise copying an errorstate vector and a covariance of the selected Kalman filter to theothers of the multiple Kalman filters.
 12. The method of claim 8,wherein determining when motion was occurring comprises determining if aposition separation between a Kalman filter that assumed no motion and aKalman filter that assumed motion is greater than a statisticallyexpected separation.
 13. The method of claim 8, wherein determining whenmotion was occurring comprises taking observations and determining ifthey exceed a threshold.
 14. A vehicle, the vehicle comprising: aninertial system that generates position information, the inertial systemcomprising: at least one inertial sensor, a processing unit, and aplurality of Kalman filters implemented in the processing unit, thatreceive information from the at least one inertial sensor, wherein atmost one of the plurality of Kalman filters has processed zero velocityupdates on the last cycle; a guidance system that communicates with theinertial system and determines a heading for the vehicle; and a positioncontroller that communicates with the guidance system and physicallymoves the vehicle in accordance with the heading determined by theguidance system.
 15. The vehicle of claim 14, wherein the system furthercomprises navigation equations that receive data from the least oneinertial sensor and integrate the received data before sending it to theplurality of Kalman filters.
 16. The vehicle of claim 14, wherein the atleast one inertial sensor is an accelerometer.
 17. The vehicle of claim14, wherein the inertial system further comprises at least one of agyroscope, an odometer, and a global positioning system.
 18. The vehicleof claim 14, wherein at least one of the plurality of Kalman filters hasnot processed zero velocity updates on the last cycle.
 19. The vehicleof claim 18, wherein at least one other of the plurality of Kalmanfilters has not processed zero velocity updates on multiple cycles. 20.The vehicle of claim 14, wherein at least one of the plurality of Kalmanfilters has not processed zero velocity updates on multiple cycles.